Seismic reflection amplitudes have now been used for 35 years in prospecting for oil and gas reserves in certain types of sedimentary rocks. For rocks with high porosities and low bulk moduli the substitution of more compressible fluids such as oil or gas for less compressible fluids such as brine results in a significant reduction in both the density and particularly the compressional wave propagation velocity. Consequently, this also impacts the acoustic impedance of such reservoir rocks, thus affecting the reflection coefficient at interfaces between them and the impermeable sealing rocks with which they are in contact. This phenomenon was described in detail in the low frequency limit by Gassmann1 and subsequently dynamically by Biot2 several decades ago. At common seismic prospecting frequencies of 10-100 Hz, the low frequency limit of Gassmann is an appropriate description for typical sedimentary rocks. For a macroscopically isotropic and homogeneous porous medium with a connected solid framework or matrix and a connected pore space in which a single pore fluid pressure can be defined, the applicable equations may be written in the form:
                    ρ        =                                            ρ              g                        ⁡                          (                              1                -                ϕ                            )                                +                                    ρ              f                        ⁢            ϕ                                              (        1        )                                                      ρ            ⁢                                                  ⁢                          V              p              2                                =                                    K              g                        [                                                                                3                    ⁢                                          (                                              1                        -                                                  v                          m                                                                    )                                                                            (                                          1                      +                                              v                        m                                                              )                                                  ⁢                β                            +                                                                    (                                          1                      -                      β                                        )                                    2                                                                      ϕ                    ⁡                                          (                                                                                                    K                            g                                                                                K                            f                                                                          -                        1                                            )                                                        +                  1                  -                  β                                                      ]                          ⁢                                  ⁢        and                            (        2        )                                                      ρ            ⁢                                                  ⁢                          V              s              2                                =                                    μ              m                        =                                          K                g                            ⁢                                                3                  ⁢                                      (                                          1                      -                                              2                        ⁢                                                  v                          m                                                                                      )                                                                    2                  ⁢                                      (                                          1                      +                                              v                        m                                                              )                                                              ⁢              β                                      ;                            (        3        )            where ρg and Kg are the density and bulk modulus respectively of the solid or granular material of which the rock matrix is constructed, ρf and Kf are the corresponding properties of the pore fluid, φ, is the porosity or fluid volume fraction of the rock, Km, μm and νm are the bulk modulus, shear modulus and Poisson's ratio respectively of the evacuated porous rock matrix, β=Km/Kg, and Vp and Vs are the compressional (P) and shear (S) wave propagation velocities in the fluid-saturated rock. If ρ, Vp and Vs are known along with the grain and fluid elastic properties for a particular pore fluid such as brine, these equations can be solved for values of the dimensionless quantities β and νm which do not depend on the pore fluid and then Vp and Vs can be calculated for a new pore fluid such as oil or gas using these values.
The critical determinant of the magnitude of the fluid substitution effect on the P-wave velocity is the Vp(φ) or equivalently, Vp(ρ), relation for the normal brine-saturated rocks at a given location. Such relations are commonly determined from wireline log measurements of both ρ and the vertical Vp made in previous wells. Of course, such relations can and do vary spatially even in the same geologic province in which neither the mineralogy nor deposition mechanism might be expected to vary significantly. It is therefore highly desirable to provide a model which can account for some of these differences, in order to be able to better account for these variations, and hence better predict the viability of potential petroleum reservoirs.
It has been known that sorting in the sedimentary rock is important in determining the permeability and hence the fluid flow which may be achieved from a well, but it has been difficult to predict permeability from measured seismic data. Empirical models have been used in the past, although these have been found not to correctly predict the density, shear velocity and compressional velocity over a range of compaction states and sorting. It is therefore particularly desirable to provide a model which can predict permeability with increased certainty on the basis of seismic data.
It has been known to model the effect of solid material in the pore space which is detached from the load-bearing matrix on the wave propagation velocities. Fabricius et al.3,4 have proposed an effective medium model to estimate these velocities in porous media in which some of the solid material is in suspension. This model, called the MUHS isoframe model, combines a solid mineral endpoint with an endpoint consisting of a suspension at critical porosity using the Hashin-Shtrikman upper bound in a procedure first proposed by Dvorkin and Nur5 for a rock with no suspended material and introduces a heuristic mixing parameter to characterize the fraction of solids in the system which are involved in load-support. The suspended solids exist in isolated pores throughout the medium so that the porous medium treated does not have one connected pore space as required to derive the Gassmann and Biot equations and thus this model is inconsistent with them. Such a model may be useful to estimate velocities in diagenetically altered carbonate rocks of low porosities with suspended solids in isolated vugular pores but is entirely inappropriate to describe the effects of fluid substitution and of suspended solids in porous and permeable hydrocarbon reservoir rocks such as those considered in relation to the present invention and will not correctly estimate these effects in them.
It is therefore desirable to provide an improved model of the effect of detached solid material in a connected pore space, which accurately models observed measurements.